The father of a missing 2-year-old whose mother's story has come under scrutiny by police believes his estranged wife may have had something to do with Sky Metalwala's disappearance.

"I do believe that Julia has a, she's responsible …," Solomon Metalwala said Wednesday, speaking of Julia Biryukova, the boy's mother. "It's sad. Because if she can just cooperate, we can find where, where is our son."

He also talked about a strange dream his wife had and which she related to him.

"In this dream she, she was strangling Sky," he said. "And it was very alarming."

Biryukova has told detectives in Bellevue, Wash., that she was driving her two children to Overlake Hospital Medical Center Sunday morning because her youngest child, Sky, wasn't feeling well.

She said she ran out of gas on 112th Avenue, so she left Sky in the car while she and her 4-year-old daughter walked about a mile away to a gas station.

When she returned to her silver Acura SUV, the child was gone, she told police.

The boy hasn't been seen since.

Investigators have serious questions about Biryukova's story. They say her account doesn't add up, and also say it's remarkably similar to an episode of the TV series "Law and Order."

The episode, which police say is "strikingly similar in nature" to Biryukova's story, centered on a mother who tries to cover up the death of her child by saying he was taken from her car.

That detail also alarms Solomon Metalwala.

"'Law and Order' was Julia's favorite show and the similarities are pretty similar and if she got that idea in her head that 'I can make this happen,' she's not going to fear the consequences, because she doesn't fear consequences," he said.

According to police, Biryukova did walk to the Northtowne Chevron Service on Sunday, but she never bought gas there, police said.

Instead, she spent time walking around a wealthy neighborhood where she reportedly didn't ask anyone for help, officials said.

When detectives checked to see how much gas was left in her car, they found enough for her to have continued driving.

Today, investigators plan to drive her car, to see if it has any mechanical problems that would have forced her to leave it on the side of the road.

Police said that after Biryukova visited the gas station she called a friend who picked her up and took her back to her two-door silver Acura, where they allegedly discovered the boy was missing.

"The story doesn't add up, the whereabouts of Sky are unknown, the mother's story is falling apart, day to day," Bellevue Police Maj. Mike Johnson said Wednesday.

Sky's father Solomon Metalwala has agreed to take two polygraph tests, but Biryukova has refused to be tested, telling investigators that she has been too disturbed to participate.

Police have made a public appeal for Biryukova's cooperation, and have also asked the public to help.

Biryukova's attorney had declined requests for comment to ABC News.

Biryukova and her husband have been locked in a difficult custody battle, during which both sides have accused the other of hurting the children, according to the Associated Press.

The Associated Press also reported that divorce papers say Biryukova had "severe" obsessive-compulsive disorder accompanied by 10-hour cleaning binges during which she would neglect her children.

A doctor, however, testified that she was still able to care for her children.

Biryukova, however, is not permitted to have contact with her daughter who will remain in foster care until the next hearing on Dec. 5.

The couple's troubled history includes a citation for leaving Sky alone in a parked car at a Target parking lot in 2009, and angry accusations hurled at each other during their divorce proceedings.